sensors

Article Potential of Pléiades and WorldView-3 Tri-Stereo DSMs to Represent Heights of Small Isolated Objects

Ana-Maria Loghin * , Johannes Otepka-Schremmer and Norbert Pfeifer Department of Geodesy and Geoinformation, Technische Universität Wien, Wiedner Hauptstraße 8-10, 1040 Vienna, Austria; [email protected] (J.O.-S.); [email protected] (N.P.) * Correspondence: [email protected]; Tel.: +43-(1)-58801-12259



Received: 30 March 2020; Accepted: 3 May 2020; Published: 9 May 2020


Abstract: High-resolution stereo and multi-view imagery are used for digital surface model (DSM) derivation over large areas for numerous applications in topography, cartography, geomorphology, and 3D surface modelling. Dense image matching is a key component in 3D reconstruction and mapping, although the 3D reconstruction process encounters difficulties for water surfaces, areas with no texture or with a repetitive pattern appearance in the images, and for very small objects. This study investigates the capabilities and limitations of space-borne very high resolution imagery, specifically Pléiades (0.70 m) and WorldView-3 (0.31 m) imagery, with respect to the automatic point cloud reconstruction of small isolated objects. For this purpose, single buildings, vehicles, and trees were analyzed. The main focus is to quantify their detectability in the photogrammetrically-derived DSMs by estimating their heights as a function of object type and size. The estimated height was investigated with respect to the following parameters: building length and width, vehicle length and width, and tree crown diameter. Manually measured object heights from the oriented images were used as a reference. We demonstrate that the DSM-based estimated height of a single object strongly depends on its size, and we quantify this effect. Starting from very small objects, which are not elevated against their surroundings, and ending with large objects, we obtained a gradual increase of the relative heights. For small vehicles, buildings, and trees (lengths <7 pixels, crown diameters <4 pixels), the Pléiades-derived DSM showed less than 20% or none of the actual object’s height. For large vehicles, buildings, and trees (lengths >14 pixels, crown diameters >7 pixels), the estimated heights were higher than 60% of the real values. In the case of the WorldView-3 derived DSM, the estimated height of small vehicles, buildings, and trees (lengths <16 pixels, crown diameters <8 pixels) was less than 50% of their actual height, whereas larger objects (lengths >33 pixels, crown diameters >16 pixels) were reconstructed at more than 90% in height.

Keywords: VHR tri-stereo satellite imagery; digital elevation model; isolated objects; dense image matching

1. Introduction For more than thirty years, civilian satellite sensors have been used for digital elevation model (DEM) extraction over large areas in a timely and cost-effective manner for a wide range of applications in engineering, land planning, and environmental management. Beginning with the year 1986, when SPOT—the first satellite providing stereo-images, with a panchromatic Ground Sampling Distance (GSD) of 10 m—was launched [1], the optical satellite industry has been experiencing continuous development. Today more and more space sensors are available that acquire not only stereo but also tri-stereo satellite imagery. The generation of high and very high resolution commercial space imaging systems for DEM generation started in September 1999, with the launch of IKONOS [2]. Among the Very High Resolution (VHR) optical satellites providing along- and across-track stereo,

Sensors 2020, 20, 2695; doi:10.3390/s20092695 www.mdpi.com/journal/sensors Sensors 2020, 20, 2695 2 of 20 the following systems can be mentioned: Ziyuan-3 (2.1 m), KOMPSAT-2 (1 m), Gaofen-2 (0.8 m), TripleSat (0.8 m), EROS B (0.7 m), KOMPSAT-3 (0.7 m), Pléiades 1A/1B (0.7 m), SuperView 1-4 (0.5 m), GeoEye-1 (0.46 m), WorldView-1/2 (0.46 m) and WorldView 3 (0.31 m). The new generation of Earth observation satellites are characterized by an increased acquisition capacity and the possibility of collecting multiple images of the same area from different viewing angles during a single pass [3,4]. This multi-view aspect is essential for extracting 3D information. In recent years, the potential of tri-stereo acquisition from high-resolution satellite images for surface modelling has become an interesting research topic that has been addressed in various publications. The capacity of the Pléiades system in performing 3D mapping was analyzed by Bernard et al. [5], where 17 images acquired from different points of view were used. They showed that by means of “triple stereo” configurations reliable digital surface models can be generated in urban areas. From their best image combination, a root mean square error (RMSE) of 0.49 m was obtained at 295 ground control points (GCPs). The radiometric and geometric characteristics of Pléiades imagery with a focus on digital surface modelling are analyzed by Poli et al. [6]. The model derived from a “triple stereo” scene (nadir, forward and backward) showed median values close to zero and an RMSE in the range of 6–7 m, when compared with a reference light detection and ranging (LiDAR) DSM. An accurate 3D map with tri-stereo images can be obtained by optimizing the sensor models with GCPs, leading to accuracies in the range of 0.5 m in planimetry and of 1 m in height as demonstrated in [7]. Much of the previous research using WorldView-3 satellite images focused on their high resolution multi-spectral information, with applications in topographic mapping, land planning, land use, land cover classification, feature extraction, change detection, and so on [8–11]. The 3D potential of WorldView-3 data is assessed by Hu et al. [12], where the reconstructed DEM shows height differences of less than 0.5 m for 82.7% of 7256 ground LiDAR checkpoints located along road axes. A new algorithm for generating high quality digital surface models is proposed by Rupnik et al. [13], where a dense image matching method is applied for multi-view satellite images from Pléiades and WorldView-3. The capability of satellite images regarding a rapid evaluation of urban environments is addressed in Abduelmula et al. [14]. They compared 3D data extracted from tri-stereo and dual stereo satellite images combined with pixel-based matching and Wallis filter to improve the accuracy of 3D models, especially in urban areas. The result showed that 3D models achieved by Pleiades tri-stereo outperformed the result obtained from a GeoEye pair, in terms of both accuracy and detail. This could mean that tri-stereo images can be successfully used for urban change analyses. The potential of VHR optical sensors for 3D city model generation has been addressed in [15–17], showing promising results for automatic building extraction when compared to a LiDAR elevation model, although highlighting some difficulties in the case of small individual house reconstruction. A quantitative and qualitative evaluation of 3D building models from different data sources was presented in [18], where a DSM at 1 m resolution derived from a GeoEye-1 stereo-pair, a DSM from an aerial block at 50 cm GSD, and a LiDAR-based DSM at 1 m resolution were used. Their results show that the percentage of correctly reconstructed models is very similar for airborne and LiDAR data (59% and 67%, respectively), while for GeoEye data it is lower (only 41%). The real dimensions of the 17 buildings surveyed were used as ground truth-reference for the 3D building model’s quality assessment, obtaining a mean value for the residual heights of 1.94 m for the photogrammetric DSM. In [19] the authors analyze and validate the potential of high-resolution DSMs produced from stereo and tri-stereo Pléiades-1B satellite imagery acquired over the Athens Metropolitan Area. From their tests, the tri-stereo model shows the best performance in height accuracy, with an RMSE of 1.17 m when compared with elevations measured by a differential global positioning system. The advantages of using tri-stereo instead of stereo image pairs are described by Piermattei et al. [20], where the nadir image increases the DSM completeness, reducing the occlusions usually caused by larger convergence angles on the ground. Additionally, they investigate in detail the influence of the acquisition geometry (viewing and incidence angles) of VHR imagery on DSM accuracy. Sensors 2020, 20, 2695 3 of 20

The cited literature concentrates on the accuracy assessments either on open areas or on (large) buildings within city areas, but not on smaller objects like cars. The standard method of DSM generation from stereo-pairs or triples is dense image matching using global or semi-global optimization. Because of the smoothness constraint of dense image matching [21], the heights of small individual objects may not be reconstructed. Hence, the corresponding 3D points will not have higher elevations compared to their surroundings. Based on this hypothesis, we investigated the capability of dense image matching when evaluating the height of small individual, i.e., detached, objects. While previous studies addressed the general 3D capabilities of VHR sensors, our investigation concentrates on small, isolated object detectability by height estimation. To the best of our knowledge, our study is the first to analyze and quantify the capability of the tri-stereo Pléiades and WorldView-3 reconstructed DSMs for single object detection by height estimation, with focus on vehicles, buildings, and trees. The object’s height compared with its surrounding terrain (in the following simply referred to as height) was investigated with respect to the following parameters: building length and width, vehicle length and width, and tree crown diameter. We investigate DSMs from different sensors with very small GSD, Pléiades and WorldView-3, but the focus is not a comparison of the two satellite systems. Specifically, our research investigation’s purpose is to answer the following questions: (1) which geometric signature and minimum size must individual objects have to be detected in the DSM-based on their reconstructed heights; and (2) what are the influences of different acquisition times, geometries, and GSDs on dense image matching quality for single objects. In the following, we first describe the tri-stereo satellite imagery used together with the study site (Section2), followed by image block orientation (in Section 3.1) using Rational Polynomial Coefficients (RPCs) and a set of GCPs. Once the orientation is completed, the 3D reconstruction follows. The 3D coordinates of the specific points corresponding to buildings, vehicles and trees are monoscopically measured in all three images: forward, nadir, and backward. The elevations obtained were used for computing the reference individual object’s height, by subtracting the correspondent elevations from a LiDAR digital terrain model (DTM) (in Section 3.2). Subsequently, the accuracy of image orientation and the procedure of dense image matching are detailed in Sections 4.1 and 4.2. After that, individual objects are grouped into different classes depending on their corresponding sizes. Their automatically-reconstructed heights are then compared with reference values (in Sections 4.3 and 4.4). Finally, the major findings of the current work are summarized in Section5.

2. Study Area and Data Analysis

The study area is located in Lower Austria, the north-eastern state of the country (48◦3003000 N; 15◦0803400 E; WGS84). With elevations ranging from 537 to 846 m above sea level, the region contains different land cover types such as: urban, suburban, rural, arable, grassland, and forested areas. Analysis was conducted based on tri-stereo satellite images acquired with both Pléiades-1B and WorldView-3 optical satellite sensors. Each triplet consists of images that were collected during the same pass from different sensor-viewing angles (along-track stereo): forward, close to nadir, and backward. The location of the study area acquired with the two sensors, with an overlapping surface of 44.5 km2, is shown in Figure1. For the current analyses, the reference data contains 43 GCPs measured by means of real time kinematic (RTK) GPS with an accuracy of approximately 1 cm. A DTM generated from a LiDAR flight campaign conducted in December 2015 is available, too. The raster DTM is in UTM 33 North map projection, datum WGS 84 with a grid spacing of 1 m. Its height accuracy was checked against the RTK GCPs yielding a σZ of 0.12 m. We used a digital orthophoto from 2017 at 0.20 m resolution for defining the positions of check points (CP). The planimetric accuracy of the digital orthophoto was verified by computing the differences between the RTK point coordinates and their corresponding position on the orthophoto. The result showed that no shifts larger than one pixel were observed. Sensors 2020, 20, x 3 of 20

The standard method of DSM generation from stereo‐pairs or triples is dense image matching using global or semi‐global optimization. Because of the smoothness constraint of dense image matching [21], the heights of small individual objects may not be reconstructed. Hence, the corresponding 3D points will not have higher elevations compared to their surroundings. Based on this hypothesis, we investigated the capability of dense image matching when evaluating the height of small individual, i.e., detached, objects. While previous studies addressed the general 3D capabilities of VHR sensors, our investigation concentrates on small, isolated object detectability by height estimation. To the best of our knowledge, our study is the first to analyze and quantify the capability of the tri‐stereo Pléiades and WorldView‐3 reconstructed DSMs for single object detection by height estimation, with focus on vehicles, buildings, and trees. The object’s height compared with its surrounding terrain (in the following simply referred to as height) was investigated with respect to the following parameters: building length and width, vehicle length and width, and tree crown diameter. We investigate DSMs from different sensors with very small GSD, Pléiades and WorldView‐3, but the focus is not a comparison of the two satellite systems. Specifically, our research investigation’s purpose is to answer the following questions: (1) which geometric signature and minimum size must individual objects have to be detected in the DSM‐based on their reconstructed heights; and (2) what are the influences of different acquisition times, geometries, and GSDs on dense image matching quality for single objects. In the following, we first describe the tri‐stereo satellite imagery used together with the study site (Section 2), followed by image block orientation (in Section 3.1) using Rational Polynomial Coefficients (RPCs) and a set of GCPs. Once the orientation is completed, the 3D reconstruction follows. The 3D coordinates of the specific points corresponding to buildings, vehicles and trees are monoscopically measured in all three images: forward, nadir, and backward. The elevations obtained were used for computing the reference individual object’s height, by subtracting the correspondent elevations from a LiDAR digital terrain model (DTM) (in Section 3.2). Subsequently, the accuracy of image orientation and the procedure of dense image matching are detailed in Sections 4.1 and 4.2. After that, individual objects are grouped into different classes depending on their corresponding sizes. Their automatically‐reconstructed heights are then compared with reference values (in Sections 4.3 and 4.4). Finally, the major findings of the current work are summarized in Section 5.

2. Study Area and Data Analysis

The study area is located in Lower Austria, the north‐eastern state of the country (48°30’30”N; 15°08’34”E; WGS84). With elevations ranging from 537 to 846 m above sea level, the region contains different land cover types such as: urban, suburban, rural, arable, grassland, and forested areas. Analysis was conducted based on tri‐stereo satellite images acquired with both Pléiades‐1B and WorldView‐3 optical satellite sensors. Each triplet consists of images that were collected during the same pass from different sensor‐viewing angles (along‐track stereo): forward, close to nadir, and backward.Sensors 2020, 20The, 2695 location of the study area acquired with the two sensors, with an overlapping surface4 of 20 of 44.5 km2, is shown in Figure 1.

Figure 1. Study area: (a) overview map of Austria with location of the study area (coordinates in UTM Figurezone 33N); 1. Study (b) satellite area: (a) imagery–blue: overview map Pl oféiades Austria tri-stereo with location pair and of orange:the study WorldView-3 area (coordinates tri-stereo in UTM pair. zone 33N); (b) satellite imagery–blue: Pléiades tri‐stereo pair and orange: WorldView‐3 tri‐stereo pair. Each satellite image was delivered with RPCs that allow the transformation between object and image space [22]. Table1 summarizes the main acquisition parameters like along, across and overall incidence angles, together with corresponding times and covered areas. Additionally, using the equations found in [23] we computed the stereo intersection angles (also called convergence angles in [24]) between each scene and their base-to-height (B/H) ratios. For WorldView-3 satellite imagery the resulting values for the B/H ratios were twice as large as those of the Pléiades imagery.

Table 1. Acquisition parameters of Pléiades and WorldView-3 data.

Sensor Type & Acquisition Time Incidence Angles (◦) Area B/H Convergence View 2 Acquisition Date (hh:hm:ss.s) Across Along Overall (km ) Ratio Angle (◦) Forward (F) 10:09:51.5 2.23 6.75 6.75 158.73 0.10 (FN) 5.71 (FN) Pléiades − − Nadir (N) 10:10:03.7 3.31 1.13 3.50 158.49 0.11 (NB) 6.30 (NB) 13-06-2017 − − Backward (B) 10:10:14.0 5.00 4.95 7.02 158.78 0.21 (FB) 12.0 (FB) − Forward (F) 10:22:07.0 7.71 11.00 13.57 100.00 0.20 (FN) 11.52 (FN) WorldView-3 Nadir (N) 10:22:25.5 7.23 0.62 7.36 100.00 0.20 (NB) 11.51 (NB) 08-04-2018 − Backward (B) 10:22:44.1 6.72 12.20 13.97 100.00 0.40 (FB) 23.04 (FB) − (FN): Forward-Nadir, (NB): Nadir-Backward and (FB): Forward-Backward image pairs.

The tri-stereo Pléiades images were provided at sensor processing level, corrected only from on-board distortions such as viewing directions and high frequency attitude variations [25]. For all three images, we performed an optical radiometric calibration using the open source software Orfeo Tool Box [26]. The pixel values were calibrated by the influence of the following parameters: sensor gain, spectral response, solar illumination, optical thickness of the atmosphere, atmospheric pressure, water vapor, and ozone amount, as well as the composition and amount of aerosol gasses. In contrast, the WorldView-3 images were delivered as tri-stereo with relative radiometrically- corrected image pixels. The relative radiometric calibration included a dark offset subtraction and a non-uniformity correction (e.g., detector-to-detector relative gain), which is performed on the raw data during the early stages of product generation. We computed the absolute radiometric calibration for each WorldView-3 image. This was done in two steps: the conversion from image pixels to top-of-atmosphere spectral radiance; and the conversion from top-of-atmosphere spectral radiance to top-of-atmosphere reflectance. The calculations were performed independently for each band, using the equations found in the technical sensor description [27]. Usually, the optical radiometric calibration step is necessary before making any physical interpretation of the pixel values. In particular, this processing is mandatory before performing any comparison of pixel spectrum between several images from the same sensor. In our case, this pre-processing step could be omitted, since it did not change the geometric quality of the images. An important characteristic of both satellites—Pléiades-1B and WorldView-3—is the fast rotation to enable recording three images within the same orbit in less than 1 min. Therefore, the images have the same illumination conditions and shadow changes are not significant. With radiometric resolutions of 16 bit/pixel, the images provide a higher dynamic range than the traditional 8- or 12-bit/pixel images. Sensors 2020, 20, 2695 5 of 20 Sensors 2020, 20, x 5 of 20

Fromradiometric a visual resolutions inspection, of some 16 radiometricbit/pixel, the eff ectsimages were provide observed a in higher the WorldView-3 dynamic range forward than image the (Figuretraditional2). Here, 8‐ or 12 the‐bit/pixel reflective images. roof surface, From a in visual combination inspection, with some the imagingradiometric incidence effects anglewere observed and sun elevation,in the WorldView caused saturation‐3 forward and image spilling (Figure effects. 2). Here, In contrast, the reflective no radiometric roof surface, artefacts in combination were observed with in the imaging incidence angle and sun elevation, caused saturation and spilling effects. In contrast, no the Pléiades satellite images. radiometric artefacts were observed in the Pléiades satellite images.

Figure 2. Detail of Pléiades (first row) and WorldView-3 (second row) tri-stereo satellite images on the Figure 2. Detail of Pléiades (first row) and WorldView‐3 (second row) tri‐stereo satellite images on same built-up area, acquired with forward-, nadir- and backward-looking. the same built‐up area, acquired with forward‐, nadir‐ and backward‐looking. 2.1. Pléiades-1B Triplet 2.1. Pléiades‐1B Triplet The Pléiades satellite system is composed of two identical satellites, Pléiades 1A/1B, which were launchedThe Pléiades by the French satellite space system agency is composed (CNES) of in two December identical 2011 satellites, and December Pléiades 1A/1B, 2012, respectively. which were Bothlaunched satellites by the are French flying onspace the agency same sun-synchronous (CNES) in December low-Earth 2011 orbitand December at an altitude 2012, of 694respectively. km with aBoth phase satellites of 18◦ areand flying an orbital on the period same ofsun 98.8‐synchronous min. The sensors low‐Earth are orbit able toat collectan altitude both of panchromatic 694 km with anda phase multispectral of 18o and images an orbital [3]. period of 98.8 min. The sensors are able to collect both panchromatic and multispectralThe Pléiades-1B images tri-stereo [3]. images used in the current investigations were acquired in the late morningThe Pléiades of 13‐ June1B tri 2017‐stereo within images 23 s. used Within in the this current time, the investigations satellite travelled were a acquired total distance in the (Base) late ofmorning 167.87 of km, 13 leadingJune 2017 to within an intersection 23 s. Within angle this of time, rays the on satellite the ground travelled of 12 ◦a. total The distance B/H ratios (Base) are ofof 0.10,167.87 0.11, km, and leading 0.21 forto an forward-nadir, intersection angle nadir-backward of rays on the and ground forward-backward of 12o. The B/H image ratios combinations. are of 0.10, The0.11, pansharpened and 0.21 for forward images composing‐nadir, nadir the‐backward triplet are and available forward in 16‐backward bit, each ofimage them combinations. with four spectral The bands,pansharpened i.e., red, images green, blue, composing and near-infrared. the triplet are Depending available onin the16 bit, viewing each of angle, them the with mean four values spectral for thebands, GSD i.e., vary red, between green, blue, 0.70 and and 0.71 near m.‐infrared. Depending on the viewing angle, the mean values for the GSD vary between 0.70 and 0.71 m. 2.2. WorldView-3 Triplet 2.2. WorldViewThe WorldView-3‐3 Triplet Digital Globe’s very high-resolution optical sensor was launched in August 2014.The Operating WorldView at an‐3 altitude Digital of Globe’s 617 km very with high an orbital‐resolution period optical of 97 sensor min, the was sensor launched provides in August 0.31 m panchromatic2014. Operating resolution. at an altitude of 617 km with an orbital period of 97 min, the sensor provides 0.31 m panchromaticAccording resolution. to the metadata, the tri-stereo WorldView-3 images for our study were acquired in springAccording 2018, on to 8 April,the metadata, within 37the s. tri‐ Thestereo corresponding WorldView‐3 base images has for a value our study of 279.69 were km acquired and the in intersectionspring 2018, angle on 8 of April, rays on within the ground 37 s. isThe 23 ◦corresponding. Even though both base sensor has a platforms value of fly279.69 at approximately km and the theintersection same speed angle (~7.5 of kmrays/s), on the WorldView-3the ground is B /H23o ratios. Even have though higher both values, sensor because platforms of the lowerfly at altitudeapproximately and increased the same acquisition speed (~ 7.5 time, km/s), compared the WorldView to the Pl‐3 éB/Hiades ratios triplet. have Hence, higher the values, B/H because ratio is 0.20of the for lower both altitude forward-nadir and increased and nadir-backward acquisition time, images, compared whereas to the for Pléiades forward-backward triplet. Hence, it the is 0.40.B/H Eachratio imageis 0.20 isfor pan-sharpened, both forward‐nadir with and four nadir spectral‐backward bands, i.e., images, red, green,whereas blue, for andforward near-infrared,‐backward with it is 16-bit0.40. Each depth image and is zero pan cloud‐sharpened, coverage. with Depending four spectral on bands, the viewing i.e., red, direction, green, blue, the meanand near GSD‐infrared, values varywith from16‐bit 0.31 depth m to and 0.32 zero m. The cloud images coverage. were deliveredDepending as eight,on the two, viewing and two direction, tiles for the close-to-nadir, mean GSD forward,values vary and from backward, 0.31 m respectively. to 0.32 m. The As aimages pre-processing were delivered step, the as tiles eight, for two, each and image two were tiles mosaicked for close‐ to‐nadir, forward, and backward, respectively. As a pre‐processing step, the tiles for each image were

Sensors 2020, 20, 2695 6 of 20

Sensors 2020, 20, x 6 of 20 accordingly. For both image triplets, Pléiades and WorldView-3, auxiliary data including the third-order rationalmosaicked function accordingly. model (RFM) For both coeffi imagecients triplets, are provided Pléiades as separateand WorldView files. ‐3, auxiliary data including theFigure third‐3order shows rational a visual function comparison model between (RFM) coefficients the pan-sharpened are provided (near) as nadirseparate images files. acquired with PléFigureiades (left)3 shows and a WorldView-3 visual comparison (right) between over a small the pan area,‐sharpened in order to (near) highlight nadir the images effects acquired of the twowith diff Pléiadeserent resolutions (left) and of WorldView 0.70 m and‐3 0.31 (right) m. Theover same a small objects area, can in order be distinguished to highlight in the both effects images: of the streets,two different buildings, resolutions cars, and of trees. 0.70 m The and higher 0.31 m. resolution The same of objects WorldView-3 can be distinguished provides a more in both detailed images: imagestreets, with buildings, clear visible cars, cars, and tree trees. branches, The higher and buildingresolution roof of edges.WorldView‐3 provides a more detailed image with clear visible cars, tree branches, and building roof edges.

(a) (b)

FigureFigure 3. 3.Comparative Comparative view view of of the the same same area area from from Pl Pléiadeséiades ( a()a) and and World World View-3 View‐3 images images ( b(b)) with with a a magnifiedmagnified detail. detail.

3.3. Data Data Processing Processing and and Analyses Analyses 3.1. Image Orientation 3.1. Image Orientation The prerequisite for a successful photogrammetric 3D reconstruction is that both interior and The prerequisite for a successful photogrammetric 3D reconstruction is that both interior and exterior orientations are correctly known. The physical sensor model based on the collinearity exterior orientations are correctly known. The physical sensor model based on the collinearity condition, describing the geometric relation between image points and their corresponding ground condition, describing the geometric relation between image points and their corresponding ground points, yields high accuracies (typically a fraction of one pixel), but is complex, and varies depending points, yields high accuracies (typically a fraction of one pixel), but is complex, and varies depending on different sensors types. Moreover, information about the camera model, ephemerides, and satellite on different sensors types. Moreover, information about the camera model, ephemerides, and attitude may not be available to users, since they are kept confidential by some commercial satellite satellite attitude may not be available to users, since they are kept confidential by some commercial image providers [28]. Usually, in practice, the RFM containing eighty RPCs is used for replacing the satellite image providers [28]. Usually, in practice, the RFM containing eighty RPCs is used for rigorous physical model of a given sensor [29]. In our research work, we have used the RFM for the replacing the rigorous physical model of a given sensor [29]. In our research work, we have used the photogrammetric mapping. RFM for the photogrammetric mapping. The workflow for DEM extraction from tri-stereo images begins with image block triangulation The workflow for DEM extraction from tri‐stereo images begins with image block triangulation and geo-referencing, based on provided RPCs and available GCPs. The main steps for the satellite and geo‐referencing, based on provided RPCs and available GCPs. The main steps for the satellite triangulation are: triangulation are: 1. 1. ImageImage point point measurement measurement of of GCPs. GCPs. The The number number of of GCPs GCPs is is di differentfferent for for the the two two image image sets sets becausebecause of of the the di differentfferent data data extent extent and and visibility visibility in in the the scenes. scenes. Therefore, Therefore, 43 43 GCPs GCPs and and 22 22 GCPs GCPs werewere manually manually measured measured in in each each Pl Pléiadeséiades and and WorldView-3 WorldView‐ tri-stereo3 tri‐stereo pair pair using using the the multi-aerial multi‐aerial viewer,viewer, which which allows allows a simultaneousa simultaneous display display of of the the images. images. This This step step is performedis performed in in order order to to stabilizestabilize the the image image block block and and to to achieve achieve higher higher accuracies accuracies by by improving improving the the given given RPCs’ RPCs’ values. values. 2. Tie points (TPs) extraction and RPC refinement. The orientation of the satellite imagery includes the automatic TPs extraction as well as an automatic and robust block adjustment. During the adjustment, a maximum number of six parameters (affine transformation in image space) can be

Sensors 2020, 20, 2695 7 of 20

2. Tie points (TPs) extraction and RPC refinement. The orientation of the satellite imagery includes the automatic TPs extraction as well as an automatic and robust block adjustment. During the adjustment, a maximum number of six parameters (affine transformation in image space) can be computed: two offsets, two drift values, and two shear values (for each image). Depending on their significance, only a subset of these corrections could be computed by the software: two shifts (on X and Y) and a scale on Y. TPs were automatically extracted by applying Feature Based Matching using the Förstner operator and refining them with Least Squares Matching [30]. TPs with residuals (in image space) larger than one pixel are considered mistakes (gross errors) and rejected. The RPCs are refined through a subsequent adjustment procedure where the differences between image- and backprojected- (with the RFM) coordinates of the GCPs and TPs are minimized. 3. Geo-positioning accuracy analysis. To evaluate the accuracy of the georeferenced images, 50 CPs were used. They were manually acquired from the available orthophoto at 0.2 m GSD and their heights were extracted at the same locations from the LiDAR DTM (1 m resolution). For CP selection, stable details on the ground such as road marks (e.g., pedestrian crossing lines), road surface changes, corners of paved areas and corners of parking lots were selected. Considering the horizontal accuracy of the orthophoto (0.10 m) and the vertical accuracy of the DTM (0.12 m), these points are less accurate than the RTK point measurements. For the current work, the entire photogrammetric workflow was implemented in the Inpho 8.0 software from Trimble [31], designed to perform precise image block triangulation through bundle block adjustment and 3D point cloud reconstruction using dense image matching techniques for push-broom cameras. The same processing line was followed for Pléiades and WorldView-3 tri-stereo images.

3.2. Manual Reference Measurements After the image orientation was completed, the manual measurement of the 3D points was performed. For each object, the highest point was selected, such as points on a building’s ridge, on a car’s roof and tree crown centre (approximation of the tree top). For the 3D restitution, we manually measured the points monoscopically in all three oriented images (forward, nadir and backward), in a multi-aerial view mode. The mean-square error of the Z object coordinate is given by the following formula [32]:

Z σZ = √2 mB σB , (1) · · · B with σZ the object elevation accuracy, σB the accuracy of image measurement (1/3rd of a pixel), Z the altitude of the satellite orbit, B the base and mB the satellite image-scale number given by the Z/c ratio, where c is the focal length of the optical system. Due to the large heights, we considered the special case of parallelism between object and image plane; hence a single scale number for the whole satellite image was used. Taking into account these parameters, the estimated accuracy of the Z object coordinates is 1.36 m and 0.31 m for the Pléiades and WorldView-3 images, respectively. These results suggest a minimum object height of 1 m as a reference height that guarantees a reasonable analysis. Since the smallest investigated cars have around 1.5 m height and buildings and single trees usually have more than 2 m height, the estimated elevation accuracy does not significantly influence our investigations. In a final step, the reference object heights are computed by using the measured Z-coordinates and the elevations extracted from the LiDAR DTM (with 1 m resolution and σZ of 0.12 m) at each point’s position. Assuming that the measured and extracted Z values have random and uncorrelated errors, according to the law of error propagation, the uncertainty associated with the manual measurements for reference object height computation is determined by the quadrature of input elevation uncertainties. The geometric parameters, i.e., vehicle length/width, tree crown diameter and building length/width, were directly measured on the rectified images in a geographic information system (GIS) environment. Sensors 2020, 20, 2695 8 of 20

Three different classes of objects were separately investigated:

(a) Vehicles are classified into four groups depending on their length: (1) passenger and family car type, smaller than 5 m; (2) vans having lengths between 5 and 7.5 m; (3) trucks with lengths between 7.5 and 10 m; and (4) articulated lorries, trailers and multi-trailers usually having more than 10 m. The lengths, widths and the corresponding elevations at car’s roofs of 50 vehicles are investigated. The computed mean reference heights are 1.5, 2.5, 3.7, and 4 m for family cars, vans, trucks, and articulated lorries, respectively. Related to average object height, the associated uncertainty of the manual height measurement varies between 8% for lorries and 22% for family cars for WorldView-3 and between 34% and 68% for Pléiades. (b) Trees are typically classified into two categories: coniferous and deciduous. Coniferous trees are cone-shaped trees, represented mainly by spruce in our case. The second category is the broad-leaved trees with leaves that fall off on a seasonal basis, mostly represented by beech and oak. We needed to perform this classification due to the different acquisition times: one in June (leaf-on conditions) and the other one in April (leaf-off conditions). The diameter and elevations were measured for 100 trees (50 trees for each category: deciduous and coniferous). Depending on crown diameters, they were grouped into seven categories, beginning with trees with a crown smaller than 2.5 m, and ending at large trees with 10 m diameter. The computed mean reference heights for the seven coniferous tree classes are: 5.5, 7.8, 11.0, 14.6, 17.2, 23.4, and 28.7 m, with uncertainties between 1% and 6% from object height for WorldView-3 and between 5% and 24% for Pléiades. The mean reference heights for the deciduous tree classes are: 3.1, 5.4, 8.0, 12.6, 15.4, 16.2, and 18.5m, with uncertainties between 2% and 10% from object height for WorldView-3 and between 7% and 44% for Pléiades. (c) For buildings, two geometrical parameters are taken into account: length and width. According to their size, built-up structures are grouped into several classes starting with very small (5 m in length and width) to large (50 m length and 25 m width). Therefore, lengths, widths, and roof ridge elevations were measured for 100 buildings in both Pléiades and WorldView-3 images. The mean reference height values varied from 2 m (small built-up structures) to 10–12 m (large industrial buildings), with associated uncertainties from 2% to 16% from object height for WorldView-3 and between 11% and 68% for Pléiades.

While identical trees and buildings were investigated in both Pléiades and WorldView-3 images, this was not possible for vehicles, since they are moving objects. Therefore, (parked) vehicles were randomly selected within the entire scene also using the non-overlapping parts.

3.3. Satellite Image Matching and 3D Reconstruction Image matching algorithms were used to identify homologous objects or pixels within the oriented images. These algorithms can be divided into area-based (e.g., [33]), feature-based (e.g., [34]), and pixel-based matching (e.g., [35]). Alternatively, image-matching approaches are often classified into sparse and dense matching or into local and global matching methods. The automatic image matching and DSM reconstruction processes were individually performed for each tri-stereo-scene (Pléiades and WorldView-3) by using the specialized module of the Inpho software, called Match-T DSM. The DSM derivation was based on three matching strategies [30]: (a) least squares matching (LSM); (b) feature-based matching (FBM) [36]; and (c) cost-based matching (CBM). Like in most image matching procedures, where image pyramids were used to reduce computation time [37], in our case, the iterative processing chain contains ten pyramid levels. On each pyramid level, three processes were performed: the matching of homologous image points, 3D intersection in object space and DEM modelling. For the first seven pyramids, FBM was used, and the last three image pyramid levels were processed with CBM. CBM is a pixel-by-pixel matching technique similar to the semi-global matching algorithm [35,38]. The CBM strategy within the Match-T DSM module uses a search-path in a so-called 3D-cost-cube for finding the corresponding pixels in images. The cost functions (e.g., correlation coefficient) are Sensors 2020, 20, 2695 9 of 20 used to find the minimum cost path, and each direction represents an X–Y movement in the image to match. Finding the pixel with the lowest cost generates a lowest-cost 3D model–surface model [30]. For each image pixel, the 3D object point coordinates were calculated by applying forward intersections, finally resulting in dense photogrammetric point clouds for the entire study area. In the last step, high resolution DSMs were generated by using the robust moving planes interpolation method. For each grid node all points within a circular neighborhood are used to robustly estimate a best fitting tilted plane (minimizing the vertical distances); points classified as outliers are not considered in the plane fitting procedure. This step was performed with the scientific software OPALS (Orientation and Processing of Airborne Laser Scanning data) [39].

4. Results and Discussion

4.1. Block Triangulation During the satellite triangulation of the tri-stereo scene, TPs were automatically extracted in each Pléiades image. They were homogenously distributed within the forward, nadir and backward images, with standard deviations of the adjusted coordinates for elevations ranging from 1.49 m (2.1 GSD) to 3.49 m (5.0 GSD) (Table2). The standard deviations of the TP elevation obtained for theWorldView-3 scenes are clearly better relative to the GSD, with a maximum value of 0.74 m (2.5 GSD). The standard deviation of the satellite image block-triangulation was 0.54 pixels for Pléiades images and 0.46 pixels for WorldView-3.

Table 2. Standard deviation of adjusted tie points (TPs) coordinates.

Standard Deviation (m/pixels) No. of Latitude Longitude Sensor Type Elevation TPs/Image (Along Track) (Across Track) min max min max min max Pléiades 561/552/582 0.16/0.23 0.33/0.47 0.14/0.20 0.27/0.38 1.49/2.12 3.49/4.98 WorldView-3 556/585/554 0.09/0.30 0.19/0.63 0.08/0.26 0.20/0.66 0.38/1.26 0.74/2.46

We evaluate the accuracy of the estimated orientation with respect to the measured GCPs and CPs. The root mean square error values of their coordinates in units of meters and pixels are shown in Table3. For both sensors the RMSE values of the GCPs for latitude, longitude and elevation are at sub-pixel level, showing that the block adjustment provides precise results for subsequent processing. The small planimetric discrepancies suggest that the GCP identification in images is better than 1/3rd of a pixel. The highest discrepancy values for the CP height are 0.85 m (1.21 GSD) for Pléiades and 0.28 m (0.93 GSD) for WorldView-3. The Pléiades elevation accuracy (0.85 m) is not as good as the one in [5], which resulted to 0.49 m, but is more favorable than the results in [7], where 1 m RMSE in elevation were reported. For WorldView-3, the vertical accuracy of 0.28 m fits to the results in [12], which reported an elevation bias of less than 0.5 m for 6001 ground LiDAR CPs. The residual errors for Pléiades images at CPs are comparable with the results obtained by [40] reporting RMSEs of 0.44 m, 0.60 m and 0.50 m at 40 GCPs for latitude, longitude and elevation, respectively.

Table 3. Root mean square error (RMSE) values of ground control point (GCP) and check point (CP) discrepancies.

RMSE Values (m/pixels) Sensor Type No. of GCPs/CPs Latitude (Along Track) Longitude (Across Track) Elevation 43 GCPs 0.20/0.29 0.19/0.27 0.27/0.39 Pléiades 50 CPs 0.44/0.63 0.53/0.76 0.85/1.21 22 GCPs 0.06/0.21 0.08/0.29 0.11/0.37 WorldView-3 50 CPs 0.13/0.43 0.12/0.40 0.28/0.93 Sensors 2020, 20, 2695 10 of 20

4.2. Dense Image Matching The dense image matching algorithm was applied individually to the two sets of image triplets available as 4-band pansharpened products. Using four cores of a 3.50 GHz machine with 32 GB RAM, the 3D point clouds were generated in 10 and 33 h for Pléiades and WorldView-3 datasets, respectively. The direct output are dense 3D photogrammetric point clouds in the LAS file format with one point for each image pixel. In the overlapping area, the Pléiades-based point cloud consists of 169 million points, whereas the WorldView-3-based equivalent has 476 million points. Hence, it’s almost three times denser. Overall, the reconstructed point clouds have a regular distribution on ground plane domain, with densities of 4 points/m2 and of 12 points/m2 for Pléiades and WorldView-3, respectively. A few small regions were not reconstructed due to occlusions (e.g., large elevation difference between buildings/trees and surrounding ground). Nevertheless, these holes were filled using interpolation algorithms in the following step. Based on a neighborhood search radius of 1 m and a maximum number of 20 nearest neighbors, we interpolated a regular grid structure using robust moving planes interpolation. For each dataset, a digital surface model was generated using the same parameters. Since we wanted to use the direct output of the 3D reconstruction without losing any information, the point clouds were not edited or filtered before the interpolation step. Usually, interpolation strategies tend to smooth the initial elevation values of the 3D point cloud. In order to minimize this effect, we selected a small size of the grid cell (0.5 m 0.5 m) and a relatively × small neighborhood definition for the interpolation. To determine the direct degree of smoothing, a raster containing the maximum elevations in each 0.5 m 0.5 m cell was computed. Using this × as a reference, the 2.5D Pléiades interpolated model showed an RMSE value of 0.079 m, while the WorldView-3 DSM had 0.098 m. The latter was slightly higher, but these values (at sub-decimetre level) still showed that the smoothing effect of the interpolation will not significantly influence further analysis. The vertical quality of the photogrammetrically derived DSMs was evaluated against the available elevations of the GCPs and CPs (Table4). The computed mean values for the CPs—0.07 m (Pl éiades) and 0.01 m (WorldView-3) and the standard deviations of 0.30 m (Pléiades) and 0.13 m (WorldView-3)—are comparable with the results obtained by [13], who reported mean values ranging between 0.08 and 0.29 m and standard deviations between 0.22 and 0.53 m. For Pléiades, we obtained an RMSE in the Z-direction of 0.29 m for GCPs and of 0.31 m for CPs. The WorldView-3 DSM showed a higher vertical accuracy, with RMSEs of 0.12 m and 0.13 m for GCPs and CPs, respectively. This is because the vertical accuracy of the DSM is directly influenced by the triplet acquisition geometry, especially by the intersection angle on the ground. As described in [41], the vertical accuracy of the DSMs from VHR satellite imagery is influenced by the acquisition geometry, where a wider angle of convergence (>15◦) enhances the height accuracy. In our case, the Pléiades scenes with a narrow convergence angle (12◦) show a lower vertical performance than the WorldView-3 scenes, with a larger convergence angle on the ground (23◦).

Table4. Vertical accuracy assessment of Pléiades and WorldView-3 tri-stereo digital surface models (DSMs).

Sensor Type No. of GCPs/CPs µ σ RMSE 43 GCPs 0.07 0.28 0.29 Pléiades 50 CPs 0.07 0.30 0.31 22 GCPs 0.03 0.18 0.12 WorldView-3 50 CPs 0.01 0.13 0.13 µ and σ are the mean and standard deviations. All values are given in meters.

The two high resolution DSMs derived from Pléiades and WorldView-3 tri-stereo scenes within the WGS84-UTM33 reference system were used as source data for the following single object investigations. Sensors 2020, 20, 2695 11 of 20

4.3. Object Height Differences For a clear height estimation, in our work we considered only single objects, located in free, open and smooth areas, without any other entities in their close surroundings. Assuming that in the free, open areas, the DSM coincide with DTM elevations, we inspected the vertical quality of the photogrammetric derived surface models by computing the vertical offsets from the reference LiDAR DTM (1 m resolution and σZ = 0.12 m). The results showed a good correspondence of the DSMs with the reference DTM, featuring a RMSE of 0.32 m for Pléiades and of 0.20 m for WorldView-3. When it comes to individual objects, we sometimes observed a constant offset, but it was always below 0.30 m. Therefore, it did not significantly impact our height investigations. The reconstructed individual object height was extracted from the interpolated surface models. Heights of buildings, vehicles and trees were computed by subtracting the DTM elevations from the elevations of the highest object points (located on roof ridges, on car roofs, and on treetops) at the same 2D location. We consider the reference height (H) as being the real object height, which was computed by subtracting the DTM elevation from the manual measurements (Section 3.2) at the same position.

H = Z Z (m) (2) M − DTM h = Z Z (m), (3) DSM − DTM with H the reference object height, h the estimated object height, ZM the manual elevation measurements, ZDTM the elevation of the ground surface and ZDSM the elevation of the reconstructed DSM. In Equations (2) and (3) the ZDTM elevation values are identical, since for computing the reference and the estimated heights, the same ground elevation at the same 2D position was considered. Based on the defined equations, we obtained a reference height (H) and two estimated heights for each individual object (from Pléiades and WorldView-3 DSMs). These values will be employed in further analysis.

4.4. Height Estimation of Single Objects Within this investigation, we wanted to estimate the Pléiades and WorldView-3 DSMs heights at single objects as a function of object type and size. For this purpose, three object types were analyzed: non-moving vehicles, trees, and buildings. The main parameters taken into account were vehicle length/width, tree crown diameter, and building length/width. For each single object, the estimated heights were compared with the monoscopic reference measurements based on a ratio measure. The percentage value derived by the following equation describes how much of the reference height was reconstructed:

p (%) = h/H 100, (4) × with H the reference height, h the estimated height, and p the reconstruction percentage.

4.4.1. Vehicles By a visual inspection of the reconstructed Pléiades-based 3D point cloud, it was observable that points corresponding to small vehicles (vehicles with lengths smaller than 5 m) were not elevated against their surroundings. Larger vehicles were reconstructed in height, but not entirely (Figure4). Sensors 20202020,, 2020,, 2695x 12 of 20

Figure 4. Height estimation for a truck. (a) Pléiades satellite image detail with profile location (left) and Figure 4. Height estimation for a truck. (a) Pléiades satellite image detail with profile location (left) reconstructed DSM Z color-coded (right); (b) WorldView-3 satellite image detail with profile location and reconstructed DSM Z color‐coded (right); (b) WorldView‐3 satellite image detail with profile (left) and reconstructed DSM Z color-coded (right); (c) Pléiades-; and (d) WV3-based vehicle profiles of location (left) and reconstructed DSM Z color‐coded (right); (c) Pléiades‐; and (d) WV3‐based vehicle 0.5 m width each from the matched point cloud; the red horizontal line is the corresponding measured profiles of 0.5 m width each from the matched point cloud; the red horizontal line is the corresponding reference height. measured reference height. Specifically, Figure4 represents a truck with a length of ~10 m and a real height of 3.5 m that Specifically, Figure 4 represents a truck with a length of ~10 m and a real height of 3.5 m that is is visible in both Pléiades (a) and WorldView-3 images (b). On the left-hand side are the magnified visible in both Pléiades (a) and WorldView‐3 images (b). On the left‐hand side are the magnified satellite image details of the vehicle and on the right-hand side are the corresponding reconstructed satellite image details of the vehicle and on the right‐hand side are the corresponding reconstructed height color-coded DSM. From the DSMs and the cross profiles (c), it is clearly visible that in contrast height color‐coded DSM. From the DSMs and the cross profiles (c), it is clearly visible that in contrast to Pléiades, where there is only ~1 m elevation change, the WV3-based profile reconstructs the vehicle to Pléiades, where there is only ~1m elevation change, the WV3‐based profile reconstructs the vehicle height up to 2.9 m, which represents ~83% of the real height. height up to 2.9 m, which represents ~83% of the real height. Using Equation (4), the height percentages of 50 measured vehicles were computed for both cases: Using Equation (4), the height percentages of 50 measured vehicles were computed for both Pléiades and WorldView-3 sensors. As mentioned in Section 3.2, vehicles were classified into four cases: Pléiades and WorldView‐3 sensors. As mentioned in Section 3.2, vehicles were classified into different groups depending on their lengths, starting with small family cars, of approximately 5 m, four different groups depending on their lengths, starting with small family cars, of approximately followed by vans, trucks, and finally by large articulated lorries with more than 10 m length. For each 5 m, followed by vans, trucks, and finally by large articulated lorries with more than 10 m length. For group, containing between 10 and 13 vehicles, the mean value of the reconstruction height percentage each group, containing between 10 and 13 vehicles, the mean value of the reconstruction height and the standard deviation were determined. They are shown in Figure5a for both Pl éiades (blue) and percentage and the standard deviation were determined. They are shown in Figure 5a for both WorldView-3 (yellow) data. By increasing length, the height percentage also increases, reaching up to Pléiades (blue) and WorldView‐3 (yellow) data. By increasing length, the height percentage also 60% (Pléiades) and 92% (WorldView-3). In the case of the Pléiades imagery, small vehicles (<7 pixels increases, reaching up to 60% (Pléiades) and 92% (WorldView‐3). In the case of the Pléiades imagery, length in image) do not show any height information, while for family cars, vans, and trucks the small vehicles (<7 pixels length in image) do not show any height information, while for family cars, reconstruction height percentage is less than 30%. It exceeds 50% only for large vehicles (lengths >10 m, vans, and trucks the reconstruction height percentage is less than 30%. It exceeds 50% only for large 14 pixels in the image). On the other hand, in WorldView-3 DSMs, vehicles have a good height vehicles (lengths >10 m, 14 pixels in the image). On the other hand, in WorldView‐3 DSMs, vehicles reconstruction (reaching over 90% for lengths >10 m, 33 pixels in image). An exception are family have a good height reconstruction (reaching over 90% for lengths >10 m, 33 pixels in image). An cars (~16 pixels length), which have a percentage of less than 40%. The standard deviations of the exception are family cars (~16 pixels length), which have a percentage of less than 40%. The standard estimated heights are notably smaller than the overall trend and they become smaller with increasing deviations of the estimated heights are notably smaller than the overall trend and they become vehicle length. smaller with increasing vehicle length. A similar analysis was conducted by using vehicle width as the main parameter for vehicle A similar analysis was conducted by using vehicle width as the main parameter for vehicle grouping (Figure5b). Because small family cars and vans have similar widths (~2 m), they form a grouping (Figure 5b). Because small family cars and vans have similar widths (~2 m), they form a single class, followed by trucks (2 to 2.5 m widths), and articulated lorries (2.5 to 3 m widths). Based on single class, followed by trucks (2 to 2.5 m widths), and articulated lorries (2.5 to 3 m widths). Based the WorldView-3 DSMs, vehicles with up to 2 m widths have ~41% of their real height reconstructed. on the WorldView‐3 DSMs, vehicles with up to 2 m widths have ~41% of their real height This value is higher when compared with the percentage of the first length-class (37%) because it reconstructed. This value is higher when compared with the percentage of the first length‐class (37%) contains both family cars and vans, leading to an increased mean height percentage and standard because it contains both family cars and vans, leading to an increased mean height percentage and deviation. The mean height percentages reach 59% (Pléiades) and 92% (WorldView-3) for the very large standard deviation. The mean height percentages reach 59% (Pléiades) and 92% (WorldView‐3) for the very large vehicles. The increased values of standard deviations suggest a higher variation of the

Sensors 2020, 20, 2695 13 of 20

Sensors 2020, 20, x 13 of 20 vehicles. The increased values of standard deviations suggest a higher variation of the reconstruction height percentages within the width-classes considered. Therefore, the length parameter is more reconstruction height percentages within the width‐classes considered. Therefore, the length suitable for the description of the vehicle’s height estimation. parameter is more suitable for the description of the vehicle’s height estimation.

Figure 5. Interval-based percentage and standard deviation for height estimation of vehicles depending onFigure (a) lengths 5. Interval and (b‐based) widths. percentage and standard deviation for height estimation of vehicles depending on (a) lengths and (b) widths. 4.4.2. Trees 4.4.2. Trees Trees were investigated in two separate classes: deciduous trees, located especially on roadsides, parksTrees and cities, were andinvestigated coniferous in trees,two separate found in classes: forested deciduous areas and trees, forest located patches. especially Only single, on roadsides, isolated trees,parks not and close cities, to and buildings coniferous or any trees, other found objects, in forested were taken areas into and consideration. forest patches. In Only this case, single, the isolated visible crowntrees, not diameter close to was buildings used as or the any geometric other objects, parameter. were taken One hundredinto consideration. trees were In investigated, this case, the and visible the samecrown formula diameter for was height used percentage as the geometric computation, parameter. Equation One hundred (4), was trees applied. were investigated, Based on diameter, and the theysame were formula grouped for height into seven percentage different computation, categories, eachEquation containing (4), was approximately applied. Based 12 on trees. diameter, The mean they reconstructionwere grouped percentagesinto seven different gradually categories, increase witheach crowncontaining diameter approximately and the standard 12 trees. deviationsThe mean decreasereconstruction (Figure percentages6). For WorldView-3, gradually theincrease heights with of coniferous crown diameter trees with and crown the standard diameters deviations<2.5 m (8decrease pixels in (Figure image space)6). For are WorldView reconstructed‐3, the less heights than 50%, of coniferous whereas trees trees with with crown crown diameters diameters larger <2.5 thanm (8 5pixels m (16 in pixels image in imagespace) space)are reconstructed are over 95%. less Generally, than 50%, heights whereas of coniferous trees with trees crown are diameters better estimated larger fromthan WorldView-35 m (16 pixels than in image from the space) Pléiades are over DSMs, 95%. where Generally, trees with heights diameters of coniferous>7.5 m (11 trees pixels) are barelybetter reachestimated 75% heightfrom WorldView reconstruction.‐3 than For from deciduous the Pléiades trees (Figure DSMs,6 b)where it can trees be observed with diameters that the >7.5 situation m (11 ispixels) reversed: barely they reach get 75% better height height reconstruction. information fromFor deciduous Pléiades DSM, trees than(Figure from 6b) WorldView-3 it can be observed DSM. Thisthat isthe mainly situation because is reversed: of the diff theyerent get acquisition better height times, information June for Pléiades from and Pléiades April forDSM, WorldView-3, than from indicatingWorldView leaf-on‐3 DSM. and This leaf-o is mainlyff conditions because which of the clearly different influence acquisition the appearance times, June and for texture Pléiades of and the treesApril in for the images.WorldView For‐ the3, deciduousindicating trees,leaf‐on only and the stemsleaf‐off and conditions branches arewhich visible clearly in the influence WorldView-3 the images,appearance resulting and intexture a poor of dense the trees image in matching the images. quality. For For the trees deciduous with a crowntrees, diameteronly the largerstems than and 9branches m, heights are of visible just over in the 50% WorldView of the tree‐ values3 images, are resulting reconstructed. in a poor dense image matching quality. For treesWhen with analyzing a crown the diameter two tree typeslarger only than from 9 m, the heights Pléiades of just images over (Figure 50% of6), the we tree could values see that are therereconstructed. is a slightly better height reconstruction for the very small and large deciduous trees, compared with theWhen coniferous. analyzing The the small two tree deciduous types only trees from in the the first Pléiades group images (with crown (Figure diameters 6), we could smaller see than that 2.5there m) is have a slightly 26% of better their height real height reconstruction reconstructed, for the whereas very small the small and coniferouslarge deciduous trees in trees, the first compared group havewith onlythe coniferous. 21%. The same The small is true deciduous for the last trees group, in wherethe first large group deciduous (with crown trees diameters (with crown smaller diameters than bigger2.5 m) than have 8.75 26% m) of have their percentages real height close reconstructed, to 80%, whereas whereas for coniferous the small theyconiferous reach only trees 75%. in the On first the othergroup hand, have for only the 21%. coniferous The same trees is of true medium for the sizes last (withgroup, crown where diameters large deciduous between trees 2.5 and (with 7.5 m)crown we obtaineddiameters better bigger height than reconstruction8.75 m) have percentages percentages close than to for 80%, the whereas deciduous. for coniferous they reach only 75%. On the other hand, for the coniferous trees of medium sizes (with crown diameters between 2.5 and 7.5 m) we obtained better height reconstruction percentages than for the deciduous.

Sensors 2020, 20, 2695x 14 of 20 Sensors 2020, 20, x 14 of 20

Figure 6. FigureFigure 6. 6.IntervalInterval-based Interval‐based‐based percentage percentage and and and standardstandard standard deviation deviation forfor for heightheight height estimation estimation estimation of of single single of single trees trees ( treesa )( a) (a) coniferous trees and (b) deciduous trees. coniferousconiferous trees trees and and (b) (b) deciduous deciduous trees. trees. Two examples of height estimation of a coniferous (Figure7) and a deciduous tree (Figure8) TwoTwo examples examples of of height height estimation estimation of of aa coniferousconiferous (Figure(Figure 7) 7) and and a a deciduous deciduous tree tree (Figure (Figure 8) 8)are are are shown. They were comparatively analyzed for Pléiades and WorldView-3 satellite images based shown.shown. They They were were comparatively comparatively analyzed analyzed forfor Pléiades andand WorldViewWorldView‐3‐ 3satellite satellite images images based based on on on both DSM and point cloud. For single coniferous trees with a 7 m crown diameter (Figure7) we bothboth DSM DSM and and point point cloud. cloud. For For single single coniferousconiferous trees withwith aa 77 mm crown crown diameter diameter (Figure (Figure 7) 7)we we achievedachieved di differentfferent results results based based on on the the inputinput data.data. From From the the true true height height of of 12.2 12.2 m, m, the the estimation estimation achieved different results based on the input data. From the true height of 12.2 m, the estimation resultedresulted in in approximately approximately 12 12 m m for for WorldView-3 WorldView‐ and3 and only only 8 m8 m for for Pl éPléiades,iades, which which represents represents 98% 98% and resulted in approximately 12 m for WorldView‐3 and only 8 m for Pléiades, which represents 98% 65%and of 65% the realof the height. real height. and 65% of the real height.

Figure 7. Height estimation of a coniferous tree with 7 m crown diameter: (a) Pléiades satellite image Figuredetail 7. (left),Height corresponding estimation ofheight a coniferous‐colored DSM tree withand profile 7 m crown location diameter: (right); ( ba) WorldView Pléiades satellite‐3 satellite image Figure 7. Height estimation of a coniferous tree with 7 m crown diameter: (a) Pléiades satellite image detailimage (left), detail corresponding (left), height‐colored height-colored DSM with DSM profile and location profile (right); location and (right); (c) tree (b profile) WorldView-3 of 0.5 m width satellite detail (left), corresponding height‐colored DSM and profile location (right); (b) WorldView‐3 satellite imagefrom detail the matched (left), height-colored point clouds; the DSM red with horizontal profile line location is the (right);measured and reference (c) tree profileheight. of 0.5 m width image detail (left), height‐colored DSM with profile location (right); and (c) tree profile of 0.5 m width from the matched point clouds; the red horizontal line is the measured reference height. fromA smallthe matched area of pointthe DSMs clouds; and the the red 3D horizontal point clouds line is generated the measured from reference the Pléiades height. and WorldView‐ 3 satelliteA small imagery area of theare shown DSMs andin Figure the 3D 8. pointThe largest clouds deciduous generated tree from with the leaves Pléiades (Figure and 8a WorldView-3 first row) A small area of the DSMs and the 3D point clouds generated from the Pléiades and WorldView‐ satellitehas a imageryreasonable are appearance shown in Figure in the8 .DSM The largestand an deciduous estimated treeheight with of leaves 14 m. (FigureMeanwhile,8a first the row) same has 3 satellite imagery are shown in Figure 8. The largest deciduous tree with leaves (Figure 8a first row) a reasonableleafless tree appearance in the WorldView in the DSM‐3 image and (Figure an estimated 8a second height row) of has 14 m.a height Meanwhile, of only theapproximately same leafless has a reasonable appearance in the DSM and an estimated height of 14 m. Meanwhile, the same tree4 inm. the A visual WorldView-3 analysis imageof height (Figure differences8a second for row)this deciduous has a height tree of and only a approximatelysmall building 4(next m. A to visual the leafless tree in the WorldView‐3 image (Figure 8a second row) has a height of only approximately analysistree) is of shown height in di twofferences profiles for (c) this and deciduous (d) in Figure tree 8. and a small building (next to the tree) is shown in 4 m. A visual analysis of height differences for this deciduous tree and a small building (next to the two profiles (c) and (d) in Figure8. tree) is shown in two profiles (c) and (d) in Figure 8.

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Figure 8. Height estimation of a deciduous tree and a small building: (a) Pléiades (first row) and Figure 8. Height estimation of a deciduous tree and a small building: (a) Pléiades (first row) and WorldView-3 (second row) views with corresponding height–color coded DSMs; (b) RGB colored 3D WorldView‐3 (second row) views with corresponding height–color coded DSMs; (b) RGB colored 3D point clouds, 1 m width height profiles from the matched point clouds; (c) for a deciduous tree; (d) for point clouds, 1 m width height profiles from the matched point clouds; (c) for a deciduous tree; (d) a small building; the red horizontal lines are the corresponding measured reference heights. for a small building; the red horizontal lines are the corresponding measured reference heights. 4.4.3. Buildings 4.4.3. Buildings The third category of objects investigated were single buildings, usually in suburban and rural areas.The They third usually category had regularof objects geometric investigated shapes, were such single as rectangles buildings, or usually squares, in which suburban facilitated and rural the visualareas. identificationThey usually ofhad the regular corresponding geometric dimensions shapes, such in the as rectifiedrectangles images. or squares, The building which facilitated length/width the werevisual measured identification in the rectified of the images,corresponding based on theirdimensions roof top in view. the For rectified buildings images. with a T-The or L-shapedbuilding plan,length/width we considered were measured the length in asthe the rectified longest images, dimension based between on their extremeroof top roofview. edges, For buildings whereas with the widtha T‐ or as L the‐shaped distance plan, across we theconsidered roof from the one length side toas the the other. longest One dimension hundred buildingsbetween extreme were chosen roof toedges, cover whereas a wide rangethe width of dimensions as the distance from across 1 to 50 the m lengthroof from (large one industrial side to the buildings) other. One and hundred widths frombuildings 1 to 25were m. chosen In the exampleto cover a shown wide range in Figure of dimensions8b, the two from small 1 buildingsto 50 m length are elevated (large industrial against theirbuildings) surroundings and widths in the from WorldView-3 1 to 25 m. data,In the which example is not shown the case in Figure for the 8b, Pl étheiades two data. small In buildings addition, theare profileelevated (d) against with two their overlaid surroundings point clouds in correspondingthe WorldView to‐3 a data, 3.6 by which 2.5 m buildingis not the clearly case revealsfor the thePléiades higher data. potential In addition, of WorldView-3 the profile sensor (d) with for height two overlaid reconstruction, point clouds as opposed corresponding to Pléiades. to a Even 3.6 by if the2.5 buildingm building edges clearly appear reveals very the smooth, higher the potential corresponding of WorldView main height‐3 sensor is still for reconstructed.height reconstruction, as opposedAgain, Equation to Pléiades. (4) was Even applied if the for building investigating edges theappear potential very of smooth, Pléiades the and corresponding WorldView-3 DSMs main forheight building’s is still reconstructed. height estimation with respect to their lengths and widths (Figure9). Based on their length,Again, we defined Equation ten (4) diff waserent applied categories, for investigating each containing the approximately potential of Pléiades ten buildings and WorldView (Figure9a).‐3 LikeDSMs in for the building’s previous height analyses estimation for vehicles with andrespect trees, to their the computed lengths and mean widths height (Figure percentages 9). Based for on buildingstheir length, show we a defined similar trend,ten different values graduallycategories, increasing each containing with building approximately length. Inten case buildings of the Pl(Figureéiades 9a). imagery, Like buildingsin the previous with lengths analyses smaller for thanvehicles 10 m and (14 pixels trees, in the image computed space) havemean a heightheight percentages for buildings show a similar trend, values gradually increasing with building length. In case of the Pléiades imagery, buildings with lengths smaller than 10 m (14 pixels in image space) have

Sensors 2020, 20, 2695 16 of 20 Sensors 2020, 20, x 16 of 20 reconstructiona height reconstruction percentage percentage of less than of less 30%, than whereas 30%, whereas buildings buildings with lengths with lengths greater greater than 5 than m have 5 m percentageshave percentages beyond beyond 50%. For 50%. both For Pl bothéiades Pléiades and WorldView-3, and WorldView buildings‐3, buildings with lengths with lengths>43 pixels >43 pixels have overhave 90% over height 90% height reconstruction. reconstruction.

FigureFigure 9. 9.Interval-based Interval‐based percentage percentage and standardand standard deviation deviation for height for estimation height estimation of buildings of depending buildings ondepending (a) lengths; on ((ba) widths.lengths; (b) widths.

Due to the lower variation in building-width, we considered only five intervals, starting from Due to the lower variation in building‐width, we considered only five intervals, starting from 0–5 m 0–5 m to 20–25 m (Figure9b). Compared with height-percentage analysis based on building length, to 20–25 m (Figure 9b). Compared with height‐percentage analysis based on building length, for the for the width parameter the situation was different. When buildings were grouped based on width parameter the situation was different. When buildings were grouped based on their their corresponding widths, we had an increased number of items within each interval (only 5 corresponding widths, we had an increased number of items within each interval (only 5 width‐ width-intervals). This led to a higher variation of height estimation percentages, and hence to higher intervals). This led to a higher variation of height estimation percentages, and hence to higher values values for the standard deviations within each interval. When analyzing the reconstruction height for the standard deviations within each interval. When analyzing the reconstruction height percentages based on the WorldView-3 images for both 0–5 m and 5–10 m length/width intervals, percentages based on the WorldView‐3 images for both 0–5 m and 5–10 m length/width intervals, we we could see higher mean values for the reconstruction percentages computed based on building could see higher mean values for the reconstruction percentages computed based on building widths. widths. Nevertheless, the corresponding standard deviations are larger in contrast to those computed Nevertheless, the corresponding standard deviations are larger in contrast to those computed on the on the length basis. The standard deviations for the length-intervals (Figure9a) become smaller with length basis. The standard deviations for the length‐intervals (Figure 9a) become smaller with increasing building length, showing a clearer trend; therefore, the length parameter gives a better increasing building length, showing a clearer trend; therefore, the length parameter gives a better estimation when analyzing the height reconstruction of buildings. estimation when analyzing the height reconstruction of buildings. The two scatter plots (Figure 10) show the relationships between building length and width The two scatter plots (Figure 10) show the relationships between building length and width and andthe reconstruction the reconstruction height height percentage. percentage. As expected, As expected, height height accuracy accuracy is better is for better WorldView for WorldView-3‐3 images imagesthan for than the for Pléiades the Plé iadesdata. data. The Thedelineation delineation lines lines separate separate the the buildings buildings with with higher higher and lowerlower reconstructionreconstruction heightheight percentagepercentage (p)(p) thanthan 50%.50%. IfIf forfor PlPléiadeséiades datadata aa 2D2D minimumminimum buildingbuilding sizesize ofof 7.5 m length by 6 m width is needed in order to get p > 50%, for WorldView-3 data only 4 m 2.5 m 7.5 m length by 6 m width is needed in order to get p > 50%, for WorldView‐3 data only 4 m× × 2.5 m isis needed.needed. p TheThe meanmean valuevalue forfor thethe residualresidual heightsheights correspondingcorresponding to to reconstructed reconstructed buildings buildings with with p> > 50%50% (of(of 2.022.02 mm forfor PlPléiadeséiades withwith 0.70.7 mm GSD)GSD) isis comparable comparable withwith thethe residualsresiduals ofof 1.941.94 mm obtainedobtained byby [[18]18] whenwhen using using a a DSM DSM from from a a GeoEye GeoEye stereo stereo pair pair (0.5 (0.5 m m GSD). GSD).

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Figure 10. Height estimation of buildings: (a) for Pléiades; (b) for WorldView-3. Figure 10. Height estimation of buildings: (a) for Pléiades; (b) for WorldView‐3. 5. Conclusions 5. Conclusions This study addresses the potential and limitations of both Pléiades and WorldView-3 tri-stereo reconstructedThis study DSMs addresses for height the potential estimation and of limitations single objects. of both Satellite Pléiades image and WorldView orientation‐3 and tri‐stereo dense imagereconstructed matching DSMs were for performed. height estimation The tri-stereo of single images objects. of each Satellite sensor image were orientation acquired in and less dense than oneimage minute, matching resulting were in performed. similar radiometric The tri‐stereo characteristics, images of a facteach that sensor is beneficial were acquired for any imagein less matchingthan one algorithm.minute, resulting For obtaining in similar higher radiometric accuracies characteristics, (at sub-pixel level a fact in that image is beneficial space and for sub-meter any image level matching in object space)algorithm. the direct For obtaining sensor orientation higher accuracies available as(at RPCs sub‐pixel is improved level in by image GCPs space through and a sub bias-compensated‐meter level in RPCobject block space) adjustment the direct. Evaluated sensor orientation at 50 CPs available in open areas,as RPCs elevation is improved accuracies by GCPs of 0.85 through m and 0.28a bias m‐ (RMSE)compensated were obtainedRPC block for adjustment. Pléiades and Evaluated WorldView-3, at 50 respectively. CPs in open areas, elevation accuracies of 0.85 mNext, and photogrammetric0.28 m (RMSE) were DSMs obtained were for generated Pléiades from and WorldView the Pléiades‐3, and respectively. WorldView-3 tri-stereo imageryNext, using photogrammetric a dense image DSMs matching were generated algorithm, from forward the Pléiades intersections, and WorldView and interpolation.‐3 tri‐stereo Theimagery estimation using a of dense a single image object’s matching height algorithm, depends onforward the accuracy intersections, of satellite and imageinterpolation. orientation, The butestimation also on of the a elevationsingle object’s accuracy height of thedepends derived on DSMsthe accuracy and on of the satellite LiDAR image reference orientation, DTM. We but found also thaton the the elevation vertical accuracy accuracy of of the the derived reference DSMs DTM and w.r.t on the LiDAR RTK GCPs reference is 0.12 DTM. m, and We thefound accuracies that the ofvertical the reconstructed accuracy of photogrammetricthe reference DTM models w.r.t the with RTK respect GCPs to theis 0.12 DTM m, are and 0.32 the m accuracies for Pléiades of andthe 0.20reconstructed m for WorldView-3 photogrammetric in open, models smooth with areas. respect The vertical to the accuracyDTM are of 0.32 the m DSMs for Pléiades from VHR and satellite 0.20 m imageryfor WorldView is influenced‐3 in open, by the smooth acquisition areas. geometry. The vertical The Pl accuracyéiades scenes of the having DSMs a narrowfrom VHR convergence satellite angleimagery of 12is ◦influencedshow a lower by the vertical acquisition performance geometry. compared The Pléiades to WorldView-3 scenes having scenes, a narrow which convergence have a 23◦ convergenceangle of 12o show angle a onlower the vertical ground. performance In addition, compared the smoothness to WorldView effect of‐3 the scenes, robust which moving have planes a 23o interpolationconvergence angle for deriving on the theground. DSMs In is addition, at sub-decimetre the smoothness level. Under effect these of the conditions, robust moving the resulting planes heightinterpolation accuracy for is deriving reasonable the and DSMs does is notat sub significantly‐decimetre influence level. Under our investigations,these conditions, since the the resulting single objectsheight accuracy measured is are reasonable usually higher and does than not 1.5 significantly m. Based on influence the different our GSDs investigations, and B/H ratios since ofthe the single two satelliteobjects measured systems, it are can usually be said higher that σ othanof block 1.5 m. adjustment, Based on the RMSE different of check GSDs point and elevation B/H ratios error of and the heighttwo satellite reconstruction systems, successit can be for said individual that σo of objects block adjustment, are similar, with RMSE deviations of check ofpoint up toelevation 20%. error and height reconstruction success for individual objects are similar, with deviations of up to 20%.

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In order to investigate the potential of Pléiades and WorldView-3 tri-stereo DSMs for single object height estimation, 50 vehicles, 100 trees, and 100 buildings were analyzed. Vehicle length/width, tree crown diameter and building length/width were identified as the main geometric parameters for classifying single objects into different groups. The results clearly show a gradual increase of the estimated heights with object dimensions. Starting from very small objects (whose heights are not reconstructed) the values for the height reconstruction percentage reached almost 100% for very large single objects (e.g., buildings with lengths >35 m in the case of WorldView-3 DSM). Hence, individual objects’ reconstructed heights strongly depend on object type, size, and the sensor being used. As an example, if we consider the p = 50% threshold for an appropriate height reconstruction, then we obtain the following minimum size values for the single objects: 10 m (Pléiades) and 5 m (WorldView-3) for vehicle lengths; 5 m (Pléiades) and 2.5 m (WorldView-3) for tree crown diameters and 7.5 m 6 m × (Pléiades) and 3.5 m 2.5 m (WorldView-3) for building length/width. The ratio of these dimensions × fits well to the GSD ratio of 70 cm to 31 cm. Generally, for all single objects except deciduous trees, the results achieved with WorldView-3 data were better than those achieved by using the Pléiades data. Hence, the ability of WorldView-3-derived DSM to perform height estimation of single objects is higher compared with Pléiades DSM. This is mainly because of the very high resolution (0.31 m) that leads (through photogrammetric processing) to very dense 3D point clouds, describing the real ground surface and the objects on it more accurately. The acquisition times also play a significant role in the photogrammetric procedure. For stable objects such as buildings, the different periods of acquisition do not affect the 3D reconstruction, but for deciduous trees, the automatic reconstructed heights are highly underestimated in the leaf-off season. Their leafless appearance in the images brings difficulties to the image matching process when finding correct correspondences for tree branches. From this observation, we can conclude that the image appearance and texture of trees (and other single objects) are also very important for the 3D reconstruction and height estimation. For all objects investigated, the resulting histograms (Figures5,6 and9 ) show interesting trends, opening new investigation options for refinement such as adding the influence of object orientation, color, and texture in the feature reconstruction ability of heights, but these are outside the scope of the present research. The poor performance on small individual objects is mainly caused by the continuity constraint of dense matching algorithms. A topic for future research would be to investigate if a combination of different matching strategies can deliver better results on single object heights. In our investigation, the current findings are valid for Pléiades and WorldView-3 DSMs derived from the tri-stereo images with their specific acquisition geometry. Nevertheless, the acquisition geometry could be changed, but this is only to a very small extend under the control of the user. A higher B/H ratio and implicit convergence angle to the ground will increase the geometric intersection quality, leading to a higher vertical accuracy of the photogrammetric DSM. This will have a positive effect on the single object height signature in the DSM. From the analyses and investigations performed, the results suggest that the acquisition geometry clearly has an effect on accuracy, but the object height estimation based on automatically derived DSMs primarily depends on object size. Objects of a few pixel in size are hardly mapped in the DSM, whereas, with some dependency on object type, objects of 12 pixels in size are typically mapped with approximately 50% of their real height. To reach 90% of the real height, a minimum object size between 15 and 30 pixel is necessary.

Author Contributions: Conceptualization, A.-M.L., J.O.-S. and N.P.; Formal analysis, A.L.; Investigation, A.-M.L.; Methodology, A.-M.L., J.O.-S. and N.P.; software, J.O.-S.; Project administration, J.O.-S.; Software, J.O.-S.; Supervision, N.P. and J.O.-S.; Validation, A.-M.L., J.O.-S. and N.P.; Visualization, A.-M.L.; Resources, J.O.-S. and N.P.; Data curation, A.-M.L., J.O.-S. and N.P.; Writing—original draft preparation, A.-M.L.; Writing—review and editing, J.O.-S. and N.P.; funding acquisition, N.P. All authors have read and agreed to the published version of the manuscript. Sensors 2020, 20, 2695 19 of 20

Funding: The work was partly funded by the Austrian Research Promotion Agency (FFG), Vienna, Austria within the research project “3D Reconstruction and Classification from Very High Resolution Satellite Imagery (ReKlaSat 3D)” (grant agreement No. 859792). Open Access Funding by TU Wien. Acknowledgments: The authors acknowledge Open Access Funding by TU Wien. We would like to thank the Institut für Militärisches Geowesen (Maximilian Göttlich and Clemens Strauß) for support in satellite image acquisition and the company Vermessung Schmid ZT GmbH (Karl Zeitlberger) for providing the RTK ground control point coordinates used in this study. Conflicts of Interest: The authors declare no conflict of interest.

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